Evaluation of Clustering Methods for Adaptive Learning Systems

Evaluation of Clustering Methods for Adaptive Learning Systems

Wilhelmiina Hämäläinen (University of Eastern Finland, Finland), Ville Kumpulainen (University of Eastern Finland, Finland) and Maxim Mozgovoy (University of Aizu, Japan)
Copyright: © 2015 |Pages: 24
DOI: 10.4018/978-1-4666-6276-6.ch014
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Abstract

Clustering student data is a central task in the educational data mining and design of intelligent learning tools. The problem is that there are thousands of clustering algorithms but no general guidelines about which method to choose. The optimal choice is of course problem- and data-dependent and can seldom be found without trying several methods. Still, the purposes of clustering students and the typical features of educational data make certain clustering methods more suitable or attractive. In this chapter, the authors evaluate the main clustering methods from this perspective. Based on the analysis, the authors suggest the most promising clustering methods for different situations.
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Introduction

Clustering student data is a central task in the educational data mining and design of intelligent learning tools. Dividing data into natural groups gives a good summary how students are learning and helps to target teaching and tutoring. This is especially topical in the domain of online adaptive learning systems due to larger amount of students and their greater diversity. Clustering can also facilitate the design of predictive models, which are the heart of intelligent tutoring systems.

Indeed, a number of scholars report successful examples of clustering (for various purposes) in actual educational environments. However, the problem of selecting the most appropriate clustering method for student data is rarely addressed. There is a plenty of mainstream clustering methods and literally thousands of specialized clustering algorithms available (Jain, 2010), and choosing the right method for the given task is not easy. In practice, researchers often just pick up the most popular k-means method without a second thought whether its underlying assumptions suit the data. In practice, this means that one may end up with an artificial partition of data instead of finding natural clusters.

The aim of the present work is to evaluate a variety of clustering methods from the perspective of clustering student data. We analyze the main approaches to clustering and see how useful models they produce and how well their underlying assumptions fit typical student data. We do not try to list as many algorithms as possible, but instead our emphasis is to describe the underlying clustering principles and evaluate their properties. Our main goal is to cover those clustering methods which are generally available in the existing data mining and statistical analysis tools, but we introduce also some promising “future methods”. Based on this analysis, we suggest the most promising clustering methods for different situations.

The rest of the chapter is organized as follows: First, we give the basic definitions, analyze domain-specific requirements for clustering methods, and survey related research. Then, we introduce the main approaches for clustering and evaluate their suitability for typical student data. Finally, we discuss future research directions and draw the final conclusions. The basic notations used in this chapter are introduced in Table 1.

Table 1.
Basic notations
NotationMeaning
mNumber of dimensions (variables)
nNumber of data points
kNumber of clusters
pi = (pi1, …, pim)Data point in m-dimensional data space
D = {p1, …, pn}Data set of n points
CiCluster
ciCluster centroid (representative point of cluster Ci)
d(pi, pj)Distance between points pi and pj
D(Ci, Cj)Distance between clusters Ci and Cj;
inter-cluster distance
|Ci|Size of cluster Ci; number of points belonging to Ci

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